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Heat

The Fourier number measures heat conducted through a body relative to heat stored, with a higher value indicating faster heat propagation. The Biot number relates the conduction resistance within a solid to the external convection resistance at the surface. A lower Biot number means conduction resistance is less important and the body can be treated as isothermal for lumped capacitance analysis. Heisler charts can be used to solve transient conduction problems by providing non-dimensionalized temperature values over time at different positions in a solid. A semi-infinite solid is one where a plane splits an infinite solid in half. Lumped system analysis assumes a uniform temperature in a body by neglecting internal conduction resistance compared to surface convection resistance.

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56 views1 page

Heat

The Fourier number measures heat conducted through a body relative to heat stored, with a higher value indicating faster heat propagation. The Biot number relates the conduction resistance within a solid to the external convection resistance at the surface. A lower Biot number means conduction resistance is less important and the body can be treated as isothermal for lumped capacitance analysis. Heisler charts can be used to solve transient conduction problems by providing non-dimensionalized temperature values over time at different positions in a solid. A semi-infinite solid is one where a plane splits an infinite solid in half. Lumped system analysis assumes a uniform temperature in a body by neglecting internal conduction resistance compared to surface convection resistance.

Uploaded by

Yohanis Agumase
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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1. Give the physical significance of: (i) Fourier number, and (ii) Biot number.

The Fourier number is a measure of heat conducted (heat penetrated) through a body relative to heat stored. A large value of the Fourier number indicates
faster propagation of heat through a body.
hLc Lc / kA Internal conduction resistance within solid
Bi   
k 1 / hA External convection resistance at body surface

Lc is a characteristic length of the body


Biot number relates between conduction resistance of a solid and convective resistance at body surface.
Bi→0: No conduction resistance at all. The body is isothermal.
Small Bi: Conduction resistance is less important. The body may still be approximated as isothermal Lumped capacitance analysis can be performed.
Large Bi: Conduction resistance is significant. The body cannot be treated as isothermal.
The smaller the Bi number, the more accurate the lumped system analysis.
It is generally accepted that lumped system analysis is applicable if Bi ≤ 0.1

When Bi £ 0.1, the temperatures within the body relative to the surroundings (i.e., T −T¥) remain within 5 percent of each other.
4. Explain in brief the use of Heisler charts in solving transient conduction heat transfer problems.
First chart in each of these figures gives the non-dimensionalised centre temperature T 0, i.e at x = 0 for the slab of thickness 2L, and at r = 0 for the cylinder
and sphere at a given time t = 0.
Temperature at any other position at the same time t, is calculated by using the second graph, called position correction chart.
The third chart is used to find Q/Qmax or Q/Q0, i.e to find the total amount of heat transfer.

5. What is an infinite and semi infinite medium and give an example for the semi-infinte solid?
Answer: A solid which extends itself infinitely in all directions of space is termed as infinite solid.
If an infinite solid is split in the middle by a plane, each half is known as semi-infinite solid.
Solidification process of the coating layer during a thermal spray operation is an unsteady heat transfer problem.
The earth can be considered to be a semi-infinite medium in determining the variation of temperature near its surface.
7. What do you mean by lumped system analysis? Explain clearly.

Interior temperatures of some bodies remain essentially uniform at all times during a heat transfer process. The temperature of such bodies are only a
function of time, T = T(t). The heat transfer analysis based on this idealization is called lumped system analysis.

Consider a body of arbitrary shape of mass m, volume V, surface area A, density ρ and specific heat Cp initially at a uniform temperature Ti.

At time t = 0, the body is placed into a medium at temperature T∞ (T∞ >Ti) with a heat transfer coefficient h. An energy balance of the solid for a time
interval dt can be expressed as:
heat transfer into the body during dt = the increase in the energy of the body during dt
h A (T∞ ‐ T) dt = m Cp dT

the assumptions made in lumped parameter analysis.

The internal conduction resistance of the body to heat flow is negligible compared to the convective resistance at the surface.

Lumped system analysis assumes a uniform temperature distribution throughout the body, which is true only when the thermal resistance of the body to
heat conduction is zero.

Example – In a heat treatment of small metal pieces, the temperature measurement with a thermocouple.

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